Andy Cohen and his newborn were photographed exclusively for PEOPLE in this week’s issue, where the new father opens up to PEOPLE and Entertainment Weekly Editorial Director Jess Cagle about becoming a dad and the powerful moment he first met his baby boy, who was born Feb. 4 via surrogate.

“I was in the delivery room. I had been hoping that he would have a full head of hair, and he really overdelivered,” jokes the Watch What Happens Livehost, 50. “That was the first thing you see, the head of hair coming out. And I was amazed.”

After Cohen “cut the umbilical cord” himself, doctors cleaned Benjamin off and brought him over to the new dad, who then went skin-to-skin with his newborn for the first time.

“He was so alert for the first two hours. His eyes were wide open. He didn’t cry; he was just calm,” Cohen recalls to PEOPLE. “I kind of have no words for it.”

Mei Tao

To bring his desire to become a dad to life, Cohen “worked with an organization that helps you find the egg donor and the surrogate, and you kind of package the whole process.”

“I worked with an incredible surrogate,” he tells PEOPLE. “She was in California. Surrogacy is illegal in so many states, including New York. I don’t understand why. It’s a voluntary process, obviously. My surrogate just viewed it as, she was giving me the ultimate gift. She gave me life. So I’ll be forever indebted to her.”

The Bravo host shares that he felt “very lucky” in that the embryo that turned into Benjamin was placed in his surrogate about a week before he turned 50 and that there were no complications, adding that he would’ve been happy with either a boy or a girl as long as it was a “healthy baby.”

“I think the biggest moment for me in the process was this summer,” Cohen recalls.

“I was shooting the Southern Charm reunion and we were on a lunch break, and my surrogate texted me a video of the first sonogram. I was in my dressing room in tears. That was the moment for me where I was like, whoa.”

Cohen may not have become a first-time parent until a little later in life than most, but the advantage of that, he tells PEOPLE, is that he has “a sense of calm that I didn’t have 10 [or] 20 years ago.”

“I think I will be [a] strict [dad], but I have a sense of what to get hysterical about and what to let slide,” he says. “I don’t want to be a helicopter dad. I don’t want to stress him out. I don’t want to stress myself out.”

“Well, that’s already happened,” the star admits of the latter reality. “That’s just part of the job.”

For more about Andy Cohen’s life as a new dad, pick up the latest issue of PEOPLE, on newsstands Friday.